D-Index & Metrics Best Publications

D-Index & Metrics D-index (Discipline H-index) only includes papers and citation values for an examined discipline in contrast to General H-index which accounts for publications across all disciplines.

Discipline name D-index D-index (Discipline H-index) only includes papers and citation values for an examined discipline in contrast to General H-index which accounts for publications across all disciplines. Citations Publications World Ranking National Ranking
Mathematics D-index 54 Citations 12,507 688 World Ranking 610 National Ranking 28

Research.com Recognitions

Awards & Achievements

2017 - SIAM Fellow For contributions to numerical methods for optimal control and model reduction.

Overview

What is he best known for?

The fields of study he is best known for:

  • Mathematical analysis
  • Quantum mechanics
  • Eigenvalues and eigenvectors

His primary areas of study are Reduction, Mathematical optimization, Numerical analysis, Applied mathematics and Algebraic Riccati equation. He is interested in Model order reduction, which is a field of Reduction. His studies in Mathematical optimization integrate themes in fields like Dynamical systems theory, Numerical stability and Numerical linear algebra.

His Numerical analysis study integrates concerns from other disciplines, such as Lyapunov equation, Lyapunov function, Iterative method and Eigenvalues and eigenvectors. His Applied mathematics study incorporates themes from Lanczos resampling and Algebraic number. His biological study spans a wide range of topics, including Invariant subspace and Linear-quadratic regulator, Linear-quadratic-Gaussian control, Optimal control.

His most cited work include:

  • A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems (671 citations)
  • Dimension Reduction of Large-Scale Systems (323 citations)
  • Dimension Reduction of Large-Scale Systems (323 citations)

What are the main themes of his work throughout his whole career to date?

His primary scientific interests are in Applied mathematics, Model order reduction, Reduction, Mathematical optimization and Mathematical analysis. His Applied mathematics research incorporates themes from Linear system, Matrix, Algebraic Riccati equation, Riccati equation and Numerical analysis. His research in Algebraic Riccati equation focuses on subjects like Algebraic number, which are connected to Newton's method.

His work is dedicated to discovering how Model order reduction, Nonlinear system are connected with Discretization and other disciplines. His work carried out in the field of Reduction brings together such families of science as Truncation, Scale, Dynamical systems theory and Interpolation. His Mathematical optimization research integrates issues from Lyapunov equation and Parallel algorithm.

He most often published in these fields:

  • Applied mathematics (47.50%)
  • Model order reduction (25.97%)
  • Reduction (25.53%)

What were the highlights of his more recent work (between 2017-2021)?

  • Applied mathematics (47.50%)
  • Model order reduction (25.97%)
  • Reduction (25.53%)

In recent papers he was focusing on the following fields of study:

Peter Benner focuses on Applied mathematics, Model order reduction, Reduction, Algorithm and Nonlinear system. His work deals with themes such as Transfer function, Matrix, Rank, Discretization and Numerical analysis, which intersect with Applied mathematics. His Numerical analysis research focuses on Scale and how it connects with Balanced truncation and Algebraic number.

His study in Model order reduction is interdisciplinary in nature, drawing from both Quadratic equation, Bilinear interpolation, Parametric statistics and Projection. His Reduction research is multidisciplinary, relying on both Structure, Dynamical systems theory, Linear system, Interpolation and Visualization. His Nonlinear system study combines topics from a wide range of disciplines, such as Differential algebraic equation, Optimal control, Boundary value problem and Robustness.

Between 2017 and 2021, his most popular works were:

  • $\mathcal H_2$-Quasi-Optimal Model Order Reduction for Quadratic-Bilinear Control Systems (32 citations)
  • Model Order Reduction : Volume 3 Applications (27 citations)
  • RADI: a low-rank ADI-type algorithm for large scale algebraic Riccati equations. (27 citations)

In his most recent research, the most cited papers focused on:

  • Quantum mechanics
  • Mathematical analysis
  • Algebra

Peter Benner mainly focuses on Applied mathematics, Model order reduction, Reduction, Algorithm and Scale. His work deals with themes such as Dynamical systems theory, Algebraic number, Riccati equation, Discretization and Numerical analysis, which intersect with Applied mathematics. His studies deal with areas such as Algebraic Riccati equation and Rank as well as Algebraic number.

His study looks at the intersection of Numerical analysis and topics like Lyapunov equation with Taylor series. His studies in Model order reduction integrate themes in fields like Basis, Transfer function, Bilinear interpolation, Computational science and Interpolation. His Reduction research integrates issues from Quadratic equation, Computation, Linear system and Observability.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

Best Publications

A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems

Peter Benner;Serkan Gugercin;Karen Willcox.
Siam Review (2015)

1271 Citations

Dimension Reduction of Large-Scale Systems

Peter Benner;Peter Benner;Volker Mehrmann;Sorensen Danny C..
(2005)

538 Citations

Numerical solution of large‐scale Lyapunov equations, Riccati equations, and linear‐quadratic optimal control problems

Peter Benner;Jing-Rebecca Li;Thilo Penzl.
Numerical Linear Algebra With Applications (2008)

378 Citations

SLICOT—A Subroutine Library in Systems and Control Theory

Peter Benner;Peter Benner;Volker Mehrmann;Vasile Sima;Sabine Van Huffel.
Applied and Computational Control, Signals, and Circuits (1999)

333 Citations

Model Order Reduction for Linear and Nonlinear Systems: A System-Theoretic Perspective

Ulrike Baur;Peter Benner;Lihong Feng.
Archives of Computational Methods in Engineering (2014)

306 Citations

Lyapunov Equations, Energy Functionals, and Model Order Reduction of Bilinear and Stochastic Systems

Peter Benner;Tobias Damm.
Siam Journal on Control and Optimization (2011)

303 Citations

Model Reduction and Approximation: Theory and Algorithms

Peter Benner;Albert Cohen;Mario Ohlberger;Karen Willcox.
(2017)

263 Citations

Interpolatory Projection Methods for Parameterized Model Reduction

Ulrike Baur;Christopher Beattie;Peter Benner;Serkan Gugercin.
SIAM Journal on Scientific Computing (2011)

247 Citations

Solving stable generalized Lyapunov equations with the matrix sign function

Peter Benner;Peter Benner;Enrique S. Quintana-Ortí.
Numerical Algorithms (1999)

211 Citations

Solving large-scale control problems

P. Benner.
IEEE Control Systems Magazine (2004)

200 Citations

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